High School Mathematics8.1 Cartesian Product of Sets

If A and B are any two sets, the set of all possible ordered pairs (a,b) with a Î A and b Î B, is called the cartesian product of A and B and is denoted by A ´ B. and it is read as A cross B.
The set builder form of A ´ B is
A ´ B = {(a,b)/a Î A and b Î B}
Observing the above relation we find the following points.
1. The ordered pair of A ´ B, the first coordinate belongs to A while the second coordinate belongs to B.
2. A ´ B ¹ B ´ A.
3. If n(A)= a and n(B) = b then n(A ´ B) = ab.
4. If A is empty or B is empty then A ´ B is empty.
5. If one of the sets A and B is infinite the other is non-empty then A ´ B is also infinite.

Q 3: If A = {1,2,3,4} and B = {6,7} then find A ´ B.{(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,5)}{(1,6),(1,8),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}{(1,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}{(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7)}

Q 4: If A = {2,3,4} and B = {5,6} then find n(A ´ B).26282524

Q 5: If A = {1,2,3} and B = {3,4} then find A ´ B.{(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)}{(1,3),(1,4),(3,2),(2,4),(3,3),(3,4)}{(1,3),(1,5),(2,3),(2,4),(3,3),(3,4)}{(1,3),(1,4),(2,3),(2,4),(3,3),(3,4)}

Q 6: If A = {2,3,4} and B = {5,6} then find A ´ B.{(2,5),(2,6),(3,6),(3,6),(4,5),(4,6)}{(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)}{(2,5),(2,6),(3,5),(3,6),(4,2),(4,6)}{(2,5),(2,4),(3,5),(3,6),(4,5),(4,6)}